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arXiv:2610.28089

Quantum Limits of Blind Superresolution Imaging

Qiushuang Lian, Jun Zhu, Liangcai Cao

Published Oct 20, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum estimation has shown that spatial-mode measurements can avoid Rayleigh's curse, but the fundamental precision limits are usually formulated for a known point-spread function (PSF). We show that, for two equally bright incoherent sources sharing an unknown static, shift-invariant complex-amplitude response, the local quantum information for separation is exactly the same as in the known-PSF case. In a quantum semiparametric formulation, the equality follows from the orthogonality of the separation score to the nuisance tangent space generated by all admissible PSF perturbations. We propose two receivers to access this information: momentum-resolved Hong--Ou--Mandel interference (MR-HOM), which acquires half the small-separation quantum information per signal photon without reconstructing the PSF, and a tomography-assisted symmetric logarithmic derivative receiver (TA-SLD), which asymptotically attains the full bound under explicit recovery conditions. These results provide a route toward blind superresolution without prior PSF calibration in microscopy, astronomy, and other optical imaging systems with uncertain responses.

DOI
10.48550/arxiv.2610.28089

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Quantum estimation has shown that spatial-mode measurements can avoid Rayleigh's curse, but the fundamental precision limits are usually formulated for a known point-spread function (PSF). We show that, for two equally bright incoherent sources sharing an unknown static, shift-invariant complex-amplitude response, the local quantum information for separation is exactly the same as in the known-PSF case. In a quantum semiparametric formulation, the equality follows from the orthogonality of the separation score to the nuisance tangent space generated by all admissible PSF perturbations. We propose two receivers to access this information: momentum-resolved Hong--Ou--Mandel interference (MR-HOM), which acquires half the small-separation quantum information per signal photon without reconstructing the PSF, and a tomography-assisted symmetric logarithmic derivative receiver (TA-SLD), which asymptotically attains the full bound under explicit recovery conditions. These results provide a route toward blind superresolution without prior PSF calibration in microscopy, astronomy, and other optical imaging systems with uncertain responses.
Quantum superresolution reveals that the vanishing of separation sensitivity in conventional imaging below the Rayleigh limit does not necessarily indicate a fundamental loss of information in the optical field. However, the quantum limit for estimating the physical distance between two incoherent point sources in three-dimensional imaging systems and its dependence on the spatial structure of the point-spread function remains largely unknown. In this work, we derive the quantum-limited precision for estimating the full distance between two incoherent point sources with arbitrary intensity imbalance in a three-dimensional spatially invariant imaging system. We show that the distance information remains finite in the sub-Rayleigh regime and is governed by the second-order displacement-response tensor of the point-spread function. The eigensystem of this tensor determines the optimal relative orientation between the two sources, and reflection symmetries of the point-spread function can further provide a simplified means of identifying the optimal orientation. This geometric structure is coordinate invariant and provides a direct strategy for improving resolution by physically rotating an anisotropic imaging system to align its optimal principal response direction with the source displacement. For a general three-dimensional Gaussian point-spread function, the response tensor is proportional to the inverse spatial covariance, establishing a direct connection between quantum-limited distance precision and the geometry of Gaussian distribution.
Superresolution has been demonstrated to overcome the limitation of Rayleigh's criterion and achieve significant precision improvement in resolving the separation of two incoherent optical point sources. However, in recent years, it was found that, if the photon numbers of two incoherent optical sources are unknown, the precision of superresolution vanishes when the photon numbers are actually different. In this work, we first analyze in detail the estimation precision of the separation for two incoherent optical sources with the same point-spread functions and show that, when the two photon numbers are different but sufficiently close, the superresolution can still be realized but with different precisions. We find the condition on how close the photon numbers need to be to realize the superresolution and derive the precision of superresolution in different regimes of the photon number difference. We further consider the superresolution for two incoherent optical sources with different point-spread functions and show that the competition between the difference of photon numbers, the difference of point-spread functions, and the separation of source locations determines the precision of superresolution. The results exhibit precision limits distinct from that of two identical point-spread functions with equal photon numbers and extend the realizable regimes of quantum superresolution. Finally, the results are illustrated by Gaussian point-spread functions. Published by the American Physical Society 2024
Quantum superresolution promises to resolve closely spaced sources beyond the diffraction limit, but existing approaches generally rely on idealized source properties or require simultaneous estimation of multiple coupled parameters of realistic sources. Here we introduce a parameter-decoupled measurement that determines the separation of realistic passive sources without estimating their unknown brightness imbalance, mutual coherence, or relative phase. A complete four-parameter quantum Fisher information analysis identifies the separation information that remains accessible in the presence of these nuisance parameters. We then construct a directly measurable log-probability invariant from projection channels whose conditional statistics depend only on the separation. Broad classes of channel pairs satisfy the resulting decoupling condition. For a Gaussian point-spread function, the lowest-order implementation asymptotically attains the four-parameter quantum limit per incident signal in the sub-Rayleigh regime. This approach converts a realistic multiparameter imaging problem into an operationally single-parameter measurement, providing a practical route toward quantum-enhanced resolution of passive spatial, temporal, and spectral signals.
The Rayleigh criterion has long served as a fundamental limit for the resolution of optical imaging. Recent advances in multiparameter quantum metrology have led to quantum superresolution that can break this limit and achieve nonvanishing precision in estimating the separation between a pair of closely located incoherent point sources. For two-dimensional optical systems, the quantum superresolution has been studied for the Cartesian components of separation between two incoherent point sources. However, the precision limit of estimating the full distance between two point sources remains unknown so far. In this paper, we investigate the estimation precision of the full distance between two incoherent point sources with arbitrary intensities in a two-dimensional imaging system. Through the multiparameter quantum estimation theory, we obtain the ultimate estimation precision for the distance and show that it remains nonzero when the distance approaches zero, which surpasses the Rayleigh criterion. We further show the dependence of the estimation precision on the relative orientation between the two point sources, which leads to a novel scheme that can enhance the precision by aligning the sources along proper directions if the point-spread functions are not circularly symmetric, and the enhancement is determined by the extent to which the point-spread functions deviate from circular symmetry. Finally, the results are illustrated by incoherent sources with Gaussian point-spread functions.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
Optical measurements that can achieve the fundamental quantum limits have the potential to improve the imaging of subdiffraction objects in important applications, including optical astronomy and fluorescence microscopy. Working towards the goal of implementing such quantum-inspired measurements for real applications, we experimentally demonstrate the localization of two incoherent optical point sources and the semiparametric estimation of object moments in the subdiffraction regime via spatial-mode demultiplexing (SPADE). In the case of two sources, we are able to estimate both of their locations accurately, not just their separation, by exploiting the asymmetric response of our SPADE device. In the case of semiparametric estimation, we demonstrate that, even if the source number is unknown, the moments of the source distribution can still be estimated accurately. Our demonstration paves the way towards the use of SPADE for optical superresolution in practical scenarios, where adaptive measurements are difficult and many parameters are unknown.